Molecular orbital calculations based on semi-empirical, ab initio, and DFT methods describe the spectroscopic properties of conjugated molecules better than simple Hückel theory.

(a) Use the computational method of your choice (semi-empirical, ab initio, or density functional methods) or your instructor’s suggestion to calculate the energy separation between the HOMO and LUMO of ethene, butadiene, hexatriene, and octatetraene.

(b) Plot the HOMO–LUMO energy separations against the experimental frequencies for π*←π ultraviolet absorptions for these molecules (61 500, 46 080, 39 750, and 32 900 cm^−1, respectively). Use mathematical software to find the polynomial equation that best fits the data.

(c) Use your polynomial fit from part (b) to estimate the wavenumber and wavelength of the π*←π ultraviolet absorption of decapentaene from the calculated HOMO–LUMO energy separation.

(d) Discuss why the calibration procedure of part (b) is necessary.